Misfiring, loses power when accelerating, jerking motion. Check engine light flashes.

the title is contradiction
" check light on, no codes."<< totally wrong
scan it one more time with a REAL scan tool this time. (there are DTC errors , or codes as you said)

what does bad idle mean? misfiring, or idle speed too low
or too high? RPM, or
surging?

say what that means please.
and more important is engine hot or cold ? failing.???? or both????
there are over 50 causes.
but can be broken down to simple physics and gauges.
1: engine bad, lost compression.
2: engine cant breath, dirty air cleaner
3: ISC stuck closed or open or just stuck. (bad idle air supply)
4: bad spark, 1 or all 4 (never had a tune in this decade.
5: cam drive, slipped (belt) causing #1 failure.
6: air fuel mix too lean, and causes rpm drop and ISC fails.
7: air fuel mix too rich and misfires.
8: egr stuck open, it misfires and ISC gives up.
9: cat clogged, engine cant breath #2 like.
10: and the vast other reasons for misfire.

we cant drive it, see it or hear it misfire, so.....????

there is a test for all 10, ask. or get car serviced.

If the engine light flashes while driving you could damage the catalyst if it's running poorly.

tune up should help, also fuel filter could be clogged and possibly fuel pump ?

Cylinders are probably misfiring. Plugs probably need changed. Also have a local parts store check for any check engine light codes. May have multiple cylinders misfiring. Could possibly be plug wires (If it has them) or the Coils on the plugs (if it is set up like this instead of plug wires).

I'm guessing you have over 100000 miles , definitely replace all the spark plugs and ignition cables and cap and rotor if your motor is such equipped. If you want a better idea of which cylinders are misfiring, go to your local Checker or Autozone and ask them for code retrieval, codes stored will give you an idea of what is failing. Code po300 is multiple misfire, po301 is cyl #1, po302 is cyl #2 and so forth.

Check Mass Airflow sensor and O2 sensors

I would check the fuel pressure first.
If the engine was miss-firing the check engine light should be on.

You have a misfiring cyclinder. check the spark plugs and wires.

check engine light on usually mean emissions. ie catalytic converter, o2 sensor.

Disconnect the battery completely, try turning the key with the battery disconnected. Put the battery back together. The check engine light should be off now..